Dynamic interfacial trapping of flexural waves in structured plates

The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions

Planning the Most Important Branch and Territorial Proportions of Social Reproduction

Implementation of the resolutions of the September (1965) Plenary Meeting of the CPSU Central Committee and transition to the branch principle of management of industry must be accompanied by further development of interbranch and interregional production ties, an increase in specialization, and an expansion of cooperation among enterprises. Favorable conditions have been created for organizing economically advantageous ties between enterprises in different economic regions while maintaining the existing rational ties within the regions.

The Interaction Between Production And Social Needs In Planned Economic Development

In its varied aspects and the mediate forms in which it is manifested, the relationship between socialist production and social needs constitutes the content of objective economic laws of socialismâin particular, the basic economic law which, as we know, predetermines the most complete satisfaction of the constantly growing material and nonmaterial needs of society through the steady growth and improvement of production. To gain a proper understanding of the role of social needs in socialist reproduction, one must at least schematically define the content of this category and the patterns that determine the volume and structure of social needs.

Truncation Effects in a Semi-infinite Periodic Array of Thin Strips: A discrete Wiener-Hopf Formulation

2rigorous solution for the current induced on a semi-infinite array of narrow metallic strips is obtained using the Wiener-Hopf factorization method in the Z-transformed domain. The method can be applied to arrays with fixed current shape on each element (e.g, single mode elements), and shows rigorously the physics of waves associated to truncated periodic structures. The solution is obtained via a rigorous factorization, that is improved by using a closed form result based on an approximated factorization. The current on the truncated array is rigorously represented as the sum of the current pertaining to the infinite array plus a contribution induced by the truncation of the array. Asymptotics shows that the truncation-induced current contribution has a diffractive behavior decaying algebraically with the element number, away from the truncation. Uniform asymptotics shows that this diffractive current is effectively represented in terms of Fresnel functions, permitting also a closed form representation in proximity of and at transverse inward resonance, i.e., when a grazing grating lobe points toward the array. Illustrative examples and comparisons with a method of moment solution show the accuracy of our results.reservedmixedF. CAPOLINO; M. ALBANIF., Capolino; Albani, Matte